We've pretty much always kept track of quotes during games in my group, dating back to the first campaign I ever ran. Usually one of the players volunteers for the responsibility, as Maggie did in the 4e game I ran over the summer. I did do the Is This Fair quotes myself, though, on the idea that the DM doesn't usually say too many funny things anyway.
We never really decided, "Oh, we should keep track of quotes," though. It's just something that happened. We kept them sporadically up until Is This Fair, and since then I've tried to make a point of it in the games I run and play in, just because they're so much fun. I enjoy going back through and reading them, my players enjoy going back through and reading them, and I've even found them a handy tool for explaining just how much fun D&D can be. They're also a fairly good way for me to remember what happened in a particular session, and they make a good cointerpoint to a more usual recap, with which I've rarely been able to capture the tone of the game.
I'm not sure why I always end up with so dang many of them, though. I don't know if it's that I have a particularly quippy group or if it's something about roleplaying or what. I'm leaning toward the roleplaying, though -- at the very least, it's a particular interaction of that group and the kind of social focus roleplaying tends to encourage. I keep quotes outside of game, too, and I don't end up with nearly as many, though I do pay closer attention when I'm gaming.
Oh, and there's Qwerty. He's good for a lot of quotes himself, and he tends to encourage that kind of behavior in others. So that's at least part of it.